Course Details

Subject {L-T-P / C} : EE6343 : Nonlinear Dynamics and Chaos: Applications to Electrical Engineering {3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Somnath Maity

Syllabus

Introduction: Phase space, deterministic versus stochastic modeling, finite vs infinite dimensional models, linear vs non-linear, autonomous vs non-autonomous systems. geometric approach to dynamical systems, fixed points, linearization, and stability

Dynamical systems: continuous vs discrete time, conservative vs dissipative Existence, uniqueness and smooth dependence of solutions of ODE's on initial conditions and parameters.

Bifurcations in one and two dimensional systems: Local vs global bifurcations, Implicit function theorem, classification of bifurcations, Some generalities: center manifold and normal form, symmetry and symmetry breaking, relation to catastrophes and sudden transitions.

Non-linear systems Analysis: Stable and unstable manifolds, conservative systems, reversible systems, Solution of (fully non-linear) damped pendulum equation, Limit cycles, relaxation oscillations, weakly non-linear oscillators, averaging method and two time-scales, Hopf bifurcation and oscillating power electrics systems, quasiperiodicity, coupled oscillators systems, nonlinear resonance and frequency locking.

Chaos and Fractal: Introduction, fixed points and cobwebs, Numerics and analysis of logistic map, periodic window, liapunov exponent, strange attractors and example. cantor sets, probabilistic constructions of fractals, fractals from deterministic systems, fractal basin boundaries, fractal dimension, correlation Dimension

Course Objectives

  1. Acquire basic knowledge of nonlinear differential equations, iterative maps, and their detailed dynamics behaviors

Course Outcomes

Expected to know about the properties of the most important strange attractors and improve their skills by solving nonlinear problems

Essential Reading

  1. S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry And Engineering”, Perscus Book Publishing Group
  2. Kathleen T. Alligood,? Tim D. Sauer and,? James A. Yorke, Chaos: An Introduction to Dynamical Systems, Springer

Supplementary Reading

  1. H. B. Stewart, J. M. T. Thompson, Nonlinear Dynamics and Chaos, Wiley and Sons, NY, USA
  2. Robert C. Hilborn, Chaos and Nonlinear Dynamics, Oxford University Press